Question : Directions: Which two signs must be interchanged to correct the following equation?
26 ÷ 24 + 6 × 27 – 105 = 29
Option 1: + and –
Option 2: ÷ and +
Option 3: + and ×
Option 4: ÷ and –
Correct Answer: ÷ and +
Solution :
Given:
26 ÷ 24 + 6 × 27 – 105 = 29
Replace the given symbols in the options one by one with the original symbols in the given equation.
First options:
+ and –
26 ÷ 24 – 6 × 27 + 105 = 29
On solving the L.H.S. of the given equation –
= 26 ÷ 24 – 6 × 27 + 105
= 1.08 – 6 × 27 + 105
= 1.08 – 162 + 105
= –55.92 ≠ 29
Second option:
÷ and +
26 + 24 ÷ 6 × 27 – 105 = 29
On solving the L.H.S. of the given equation –
= 26 + 24 ÷ 6 × 27 – 105
= 26 + 4 × 27 – 105
= 26 + 108 – 105
= 29
Third option:
+ and ×
26 ÷ 24 × 6 + 27 – 105 = 29
On solving the L.H.S. of the given equation –
= 26 ÷ 24 × 6 + 27 – 105
= 1.08 × 6 + 27 – 105
= 6.48 + 27 – 105
= –71.52 ≠ 29
Fourth option:
÷ and –
26 – 24 + 6 × 27 ÷ 105 = 29
On solving the L.H.S. of the given equation –
= 26 – 24 + 6 × 27 ÷ 105
= 26 – 24 + 6 × 0.257
= 26 – 24 + 1.542
= 3.542 ≠ 29
So, the second option satisfies the equation. Hence, the second option is correct.
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